Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “partial least squares”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Simulation and study of small numbers of random events

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

Shelton, R. D.↗
NASA NTRS1988

GaussFit - A system for least squares and robust estimation

GaussFit is a new computer program for solving least-squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.

Jefferys, W. H.↗
NASA NTRS2004

An Evaluation of Quantitative Methods of Determining the Degree of Melting Experienced by a Chondrule

Many workers have considered the degree to which partial melting occurred in chondrules they have studied, and this has led to attempts to find reliable methods of determining the degree of melting. At least two quantitative methods have been used in the literature: a convolution index (CVI), which is a ratio of the perimeter of the chondrule as seen in thin section divided by the perimeter of a circle with the same area as the chondrule, and nominal grain size (NGS), which is the inverse square root of the number density of olivines and pyroxenes in a chondrule (again, as seen in thin section). We have evaluated both nominal grain size and convolution index as melting indicators. Nominal grain size was measured on the results of a set of dynamic crystallization experiments previously described, where aliquots of LEW97008(L3.4) were heated to peak temperatures of 1250, 1350, 1370, and 1450 C, representing varying degrees of partial melting of the starting material. Nominal grain size numbers should correlate with peak temperature (and therefore degree of partial melting) if it is a good melting indicator. The convolution index is not directly testable with these experiments because the experiments do not actually create chondrules (and therefore they have no outline on which to measure a CVI). Thus we had no means to directly test how well the CVI predicted different degrees of melting. Therefore, we discuss the use of the CVI measurement and support the discussion with X-ray Computed Tomography (CT) data.

Nettles, J. W.↗
NASA NTRS1997

Exponential Approximations Using Fourier Series Partial Sums

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Banerjee, Nana S.↗
NASA NTRS1993

Improved Nystrom Integrators

New formulation for Nystrom integrators offers increased precision and speed of computation. Formulation takes advantage of capabilities of modern electronic computers. Independent and dependent variables and various partial and total derivatives expressed via compact tensor notation. In this approach, typical set of constraint equations derived in about 1 day. Solution of constraint equations speeded by SEARCH computer program. Is general-purpose optimization program, which maximizes or minimizes cost function defined by user. Used successfully, to make least-squares fit of about 4,000 equations in 12 unknowns.

Lear, William M.↗
NASA NTRS1992

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Wathen, A. J.↗
NASA NTRS1986

Open system magnetic evolution of the taos plateau volcanic field, Northern New Mexico. I - The petrology and geochemistry of the servilleta basalt

MULTIFIT, an embodiment of the conceptual structure needed in modeling multisource and multiprocess magmatic systems, is described. This program, which uses familiar materials balance methodology and the equilibrium form of the Rayleigh equations, links evolutionary arrays, which is turn collectively relate the starting and final compositions of a given magmatic system. Moreover, MULTIFIT incorporates variations within major element data arrays; the linkage between them can be tested using an extension of the least squares algorithm, which selects the best branch point according to the minimum-sum-of-squared-residuals criterion. Advantages and disadvantages of the materials balance approach used in this program are discussed, an example is provided, and equations utilized by MULTIFIT are summarized. While MULTIFIT may not be the best approach for poorly constrained models involving partial melting for complex mixing, it may ultimately prove useful for ascertaining trace element partition coefficients in magnetic systems.

Dungan, M. A.↗
NASA NTRS1988

Kinetics of thermochemical gas-solid reactions important in the Venus sulfur cycle

The thermochemical net reaction CaCO3 + SO2 yields CaSO4 + CO is predicted to be an important sink for incorporation of SO2 into the Venus crust. The reaction rate law was established to understand the dependence of rate on experimental variables such as temperature and partial pressure of SO2, CO2, and O2. The experimental approach was a variant of the thermogravimetric method often employed to study the kinetics of thermochemical gas-solid reactions. Clear calcite crystals were heated at constant temperature in SO2-bearing gas streams for varying time periods. Reaction rate was determined by three independent methods. A weighted linear least squares fit to all rate data yielded a rate equation. Based on the Venera 13, 14 and Vega 2 observations of CaO content of the Venus atmosphere, SO2 at the calculated rate would be removed from the Venus atmosphere in about 1,900,00 years. The most plausible endogenic source of the sulfur needed to replenish atmospheric SO2 is volcanism. The annual amount of erupted material needed for the replenishment depends on sulfur content; three ratios are used to calculate rates ranging from 0.4 to 11 cu km/year. This geochemically derived volcanism rate can be used to test if geophysically derived rates are correct. The work also suggests that Venus is less volcanically active than the Earth.

Fegley, Bruce, Jr.↗
NASA NTRS1975

Computer-oriented synthesis of wide-band non-uniform negative resistance amplifiers

This paper presents a synthesis procedure which provides design values for broad-band amplifiers using non-uniform negative resistance devices. Employing a weighted least squares optimization scheme, the technique, based on an extension of procedures for uniform negative resistance devices, is capable of providing designs for a variety of matching network topologies. It also provides, for the first time, quantitative results for predicting the effects of parameter element variations on overall amplifier performance. The technique is also unique in that it employs exact partial derivatives for optimization and sensitivity computation. In comparison with conventional procedures, significantly improved broad-band designs are shown to result.

Branner, G. R.↗
NASA NTRS2007

Sensitivity Testing of the NSTAR Ion Thruster

During the Extended Life Test of the DS1 flight spare ion thruster, the engine was subjected to sensitvity testing in order to characterize the macroscopic dependence of discharge chamber sensitivity to a +\-3% vatiation in main flow, cathode flow and beam current, and to +\5% variation in beam and accelerator voltage, was determined for the minimum- (THO), half- (TH8) and full power (TH15) throttle levels. For each power level investigared, 16 high/low operating conditions were chosen to vary the flows, beam current, and grid voltages in in a matrix that mapped out the entire parameter space. The matrix of data generated was used to determine the partial derivative or senitivity of the dependent parameters--discharge voltage, discharge current, discharge loss, double-to-single-ion current ratio, and neutralizer-keeper voltage--to the variation in the independent parameters--main flow, cathode flow, beam current, and beam voltage. The sensititivities of each dependent parameter with respect to each independent parameter were determined using a least-square fit routine. Variation in these sensitivities with thruster runtime was recorded over the duration of the ELT, to detemine if discharge performance changed with thruster wear. Several key findings have been ascertained from the sensitivity testing. Discharge operation is most sensitve to changes in cathode flow and to a lesser degree main flow. The data also confirms that for the NSTAR configuration plasma production is limited by primary electron input due to the fixed neutral population. Key sensitivities along with their change with thruster wear (operating time) will be presented. In addition double ion content measurements with an ExB probe will also be presented to illustrate beam ion production and content sensitivity to the discharge chamber operating parameteres.

electric propulsion↗
NASA NTRS1982

Toward autonomous spacecraft

Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented.

Fogel, L. J.↗
NASA NTRS1992

Aperture codes for sensors viewing extended objects from space

The paper describes aperture codes viewing extended objects form space which find application in imaging an extended object which may have relatively low contrast, and whose lateral limits extend beyond the FOV of the sensor. Those elements of an extended object lying near the FOV limits are only partially coded, i.e., flux from those elements cannot cast a shadow of the entire aperture code onto the detector, as can elements near the center of the FOV. This has consequences for the algorithms used to reconstruct the image. The object field is divided into a number of elements which is smaller than the number of detector pixels, and a least squares fit to the data is performed. The methods used for choosing the matrices representing the aperture codes are discussed, and computer simulations of the effects of noise are described.

Curtis, C. C.↗
NASA NTRS1998

Empirical correction for earth sensor horizon radiance variation

A major limitation on the use of infrared horizon sensors for attitude determination is the variability of the height of the infrared Earth horizon. This variation includes a climatological component and a stochastic component of approximately equal importance. The climatological component shows regular variation with season and latitude. Models based on historical measurements have been used to compensate for these systematic changes. The stochastic component is analogous to tropospheric weather. It can cause extreme, localized changes that for a period of days, overwhelm the climatological variation. An algorithm has been developed to compensate partially for the climatological variation of horizon height and at least to mitigate the stochastic variation. This method uses attitude and horizon sensor data from spacecraft to update a horizon height history as a function of latitude. For spacecraft that depend on horizon sensors for their attitudes (such as the Total Ozone Mapping Spectrometer-Earth Probe-TOMS-EP) a batch least squares attitude determination system is used. It is assumed that minimizing the average sensor residual throughout a full orbit of data results in attitudes that are nearly independent of local horizon height variations. The method depends on the additional assumption that the mean horizon height over all latitudes is approximately independent of season. Using these assumptions, the method yields the latitude dependent portion of local horizon height variations. This paper describes the algorithm used to generate an empirical horizon height. Ideally, an international horizon height database could be established that would rapidly merge data from various spacecraft to provide timely corrections that could be used by all.

Hashmall, Joseph A.↗
NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Jiang, Bo-Nan↗
NASA NTRS1995

Fitting Prony Series To Data On Viscoelastic Materials

Improved method of fitting Prony series to data on viscoelastic materials involves use of least-squares optimization techniques. Based on optimization techniques yields closer correlation with data than traditional method. Involves no assumptions regarding the gamma'(sub i)s and higher-order terms, and provides for as many Prony terms as needed to represent higher-order subtleties in data. Curve-fitting problem treated as design-optimization problem and solved by use of partially-constrained-optimization techniques.

Hill, S. A.↗
NASA NTRS1986

Static shape control for flexible structures

An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.

Rodriguez, G.↗
NASA NTRS1987

Studies of outer planet satellites, Mercury and Uranus

Arguments were made, based on geometry, for both an impact and an internal origin for the ancient, partially preserved furrow system of Ganymede. It was concluded that furrows were not concentric, but could be impact related if multiringed structures on icy satellites are initially noncircular. The geometry of the Valhalla ring structure on Callisto was examined in order to assess the circularity of an unmodified ring system. The Ganymede furrow system was remapped to make use of improvements in coordinate control. The least-squares center of curvature for all furrows in the Marius and Galileao Regio is -20.7, and 179.2 degrees. Furrows in Marius and Galileo Regio are reasonably concentric, and are much more circular than previously estimated. The perceived present nonalignment of the assumed originally concentric furrows were used to argue for large-scale lateral motion of dark terrain blocks in Ganymede's crust, presumably in association with bright terrain formation., The overall alignment of furrows as well as the inherent scatter in centers of curvature from subregions of Galileo and Marius do not support this hypothesis.

Mckinnon, William B.↗
NASA NTRS1973

Prototype partial one-third octave band spectrum analyzer for acoustic, vibration and other wideband data for flight applications

The design refinement of a compact frequency analyzer for measurement and analysis on board flight vehicles is discussed. The analyzer has been constructed in a partial one-third octave band configuration with six filters and detectors spaced by the square root of 10 from 316 Hz to 100,000 Hz and a broadband detector channel. The analyzer has been tested over a temperature range of 40 to 120 F at a pressure of one atmosphere, and at a temperature of 75 F at an absolute pressure of 0.000001 torr, and has demonstrated at least 60 db of dynamic range.

Source record↗